Xah Programing Blog 2014-11

2014-11-28

linux systemd is wreaking serious havok in Linux community. Now Debian is forking. How i wish i can understand it, or, have any clue about system programing, or, how kernal, cpu, memory, assembly, etc low-level stuff works.

but life is short. I don't envision i'll ever go down this path. What remaining time i have in life i'll keep at high-level math stuff. Recursion theory, parser, math, proof systems, etc.

xah's rumination extempore: on Turing Machine being a misfit in terminology and ontology of theory of computation

(note: “xah's rumination extempore” is when i type as fast as i can of my brain flow for fun and profit)

when intro to “turing machine” in comp theory, the term is illogical, out of blue. For example, why not elephant, or ghosts? we want the ontology of things. what this “machine” thing relates to comp theory.

even “Turing model of algorithm” is bad, because the word “model”, like wtf is that?

ok, it's like this. Suppose we are discussing which restaurant to go to. I say McDonalds, some said Kenturkey Chicken, some say Donking Donuts, some said TGI Fridays, some said the local restauraunt, but then, somebody said pizza!

now, you see that's out of the blue. That doesn't fit. The fitting set are restaunraunt names, but out comes a food name. That's outside the system.

So, when discussing theory computation, introducing Turing Machine, is like that, in about 99.99999% of books. (assuming here we are following a logical style of a treaties on theory of computation).

note that, intuitively we understand it. As soon as people learned what Turing machine is, we can see how it fits into computer science. But, the point of this article, is that it is not a systematic logical approach of things.

what we want, is a ontology of things. So, when talking about theory of computation, we'd like to establish first that what it is. (that is, in more severe degree, we want a so-called mathematical formal definition. Or, in a extreme case, we want symbolic logic.)

once we know what it is, then, we may in due course introduce different topic, such as Turing Machine, and we can see, exactly, how it fits in. That is, ontology.

so, what's the relation of “turing machine” to theory of computation? we need to think about that. Remember, that we all intuitive know what the relation is. The problem, is to come up with explicit relation, which also means a lot explicit definition, thinking a lot about it.

in a few minutes, am thinking “turinig machine” is best termed “turing model of algorithm”. But that doesn't exactly work, because then what does “model” means? I also thought, “turing machine” is best characterized simply as “algorithm”, but that's not right, because that's not a specific algorithm or the general sense of algorithm; it is NOT a algorithm.

PS: ah，a epiphany❕ theory of computation includes a hardware，of which algorithm works on，we call “machine”。That's how Turing Machine fits。yay❕

2014-11-23

indicator function

comp sci terminology: a indicator function is a function f that returns either true or false, with true meaning the input is a member of a particular set.

the function f is either used as a definition that defines a set, or as problem of finding a way to construct the set. (the set may be well-defined yet we don't know its members. (For example, solution of a equation of 1 variable))